Distribution of Energy Spectra in a LargejShell

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Abstract
The validity of a gaussian distribution of energy spectra is studied with the help of closed algebraic expressions of the first four moments of energy spectra. We consider a jn configuration of identical particles, where j is very large. As a two-body interaction, a quadrupole-quadrupole interaction and several types of random interactions are used. For j →∞ we derive a simple and general condition for an interaction to produce an energy spectrum which is close to a gaussian distribution, so long as the first four moments are concerned. The interaction which induces a nuclear collective motion yields strong deviation from a gaussian distribution.

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